Do the circles x^2 + y^2 = 36 and x^2 + y^2 + 2x = 35 intersect each other

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of a circle with center (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.

The circle x^2 + y^21 = 36 is centered at (0, 0) and has a radius 6.

x^2 + y^2 + 2x = 35

=> x^2 + 2x + 1 + y^2 = 36

=> (x + 1)^2 + y^2 = 36

This is a circle centered at (-1, 0) and has a radius 6. As the center of the circles are at a distance of 1 and their radius is equal the two intersect each other.

The circles x^2 + y^2 = 36 and x^2 + y^2 + 2x = 35 intersect each other

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